Dynamic spatial-mode allocation in an under-addressed optical mimo system

ABSTRACT

The outage probability in an under-addressed optical MIMO system may be reduced by configuring a spatial-mode coupler at a transmitter and/or a spatial-mode separator at a receiver to dynamically change its spatial-mode configuration on a time scale that is shorter than the channel coherence time. Provided that the MIMO system employs an FEC code that has a sufficient error-correcting capacity for correcting the amount of errors corresponding to an average state of the MIMO channel established between the transmitter and receiver, this relatively fast dynamic change tends to reduce the frequency of events during which the number of errors per FEC-encoded block of data exceeds the error-correcting capacity of the FEC code.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. Provisional PatentApplication No. 61/449,246, filed Mar. 4, 2011, and entitled“SPATIAL-MODE MANAGEMENT IN UNDER-ADDRESSED OPTICAL MIMO SYSTEMS,” whichis incorporated herein by reference in its entirety.

The subject matter of this application is related to that of U.S. patentapplication Ser. No. ______, by Peter J. Winzer and Gerard J. Foschini,attorney docket reference 809976-US-NP, filed on the same date as thepresent application, and entitled “INTRA-LINK SPATIAL-MODE MIXING IN ANUNDER-ADDRESSED OPTICAL MIMO SYSTEM,” which is incorporated herein byreference in its entirety.

BACKGROUND

1. Field of the Invention

The present invention relates to optical communication equipment and,more specifically but not exclusively, to equipment for establishing andoperating multiple-input/multiple-output (MIMO) optical-transportchannels over a multimode or multi-core fiber.

2. Description of the Related Art

This section introduces aspects that may help facilitate a betterunderstanding of the invention(s). Accordingly, the statements of thissection are to be read in this light and are not to be understood asadmissions about what is in the prior art or what is not in the priorart.

MIMO methods are being actively developed to exploit the inherently hightransmission capacity of multimode and multi-core optical fibers. At atransmitter of an optical MIMO system, a plurality of optical signalsare independently modulated with data and coupled into a correspondingplurality of spatial modes of a multimode or multi-core fiber fortransmission to a remote receiver. At the receiver, the received opticalsignals carried by the plurality of spatial modes are separated from oneanother and demodulated/decoded to recover the data encoded onto theoriginal optical signals at the receiver.

A representative multimode or multi-core fiber used in an optical MIMOsystem may have a relatively large number of (e.g., >100) spatial modes.Due to certain hardware limitations, a conventional transmitter may notbe able to individually address all of the spatial modes supported by atypical multimode or multi-core fiber. For similar hardware reasons, aconventional receiver also may not be able to individually address allof those supported spatial modes. As a result, such a transmitter maynot be able to simultaneously couple corresponding modulated opticalsignals into all of the supported spatial modes, and such a receiver maynot be able to simultaneously extract corresponding modulated opticalsignals from all of the supported spatial modes. In addition, the subsetof spatial modes addressed at the transmitter may differ from the subsetof spatial modes addressed at the receiver. Disadvantageously, theoptical noise and mode-dependent loss imposed by the fiber-optic linkmay cause the outage probability in such an under-addressed optical MIMOsystem to be relatively high.

SUMMARY

These and certain other problems in the prior art are addressed byvarious embodiments of an optical MIMO system disclosed herein.Innovative aspects of this disclosure include, but are not limited to:(i) an optical MIMO system designed and configured to dynamically andintelligently manage the spatial-mode selection/allocation at atransmitter and/or receiver of optical space-division-multiplexed (SDM)signals, (ii) an intra-link optical mode mixer designed and configuredto controllably alter the spatial-mode mixing characteristics of theoptical link, and (iii) methods of operating the system as a whole and,also, each of the transmitter, receiver, and mode mixer individually toachieve a high transmission capacity and/or high reliability ofoperation. Certain benefits and advantages provided by variousembodiments of the disclosure may become especially pronounced when thesystem specifications impose a relatively stringent bit-error rate (BER)requirement.

According to one aspect of the disclosure, the outage probability in anunder-addressed optical MIMO system may be reduced by configuring aspatial-mode coupler at a transmitter or a spatial-mode separator at areceiver to dynamically change its spatial-mode configuration on a timescale that is faster than the channel coherence time. Provided that theMIMO system employs an FEC (forward error correction) code that has asufficient error-correcting capacity for correcting the amount of errorscorresponding to an average state of the MIMO channel establishedbetween the transmitter and receiver, this relatively fast dynamicchange tends to reduce the frequency of events during which the numberof errors per FEC-encoded block of data exceeds the error-correctingcapacity of the FEC code.

According to one embodiment, provided is an optical system having anoptical-mode-coupling (OMC) device configured to address a first subsetof spatial modes of an optical link; and a controller configured toreconfigure the OMC device to address a second subset of spatial modesof the optical link during transmission of an optical signal carryingdata through said OMC device and said optical link, wherein the secondsubset differs from the first subset by one or more spatial modes.

In some embodiments of the above optical system, the optical linkcomprises a multimode fiber, a multi-core fiber, or a fiber-optic cable;and the OMC device is configured to address a subset of spatial modes ofsaid multimode fiber, multi-core fiber, or fiber-optic cable.

In some embodiments of any of the above optical systems, the datacomprises an FEC-encoded block of data or a pilot data sequence.

In some embodiments of any of the above optical systems, the controlleris configured to cause the OMC device to change the addressing of thespatial modes at a rate that is greater than an inverse of a channelcoherence time corresponding to the optical link.

In some embodiments of any of the above optical systems, the OMC deviceis a spatial-mode coupler of an optical transmitter.

In some embodiments of any of the above optical systems, the opticalsystem further comprises: an FEC encoder configured to generate aplurality of data streams carrying an FEC-encoded block of data; and anE/O converter configured to convert said plurality of data streams intoa plurality of modulated optical signals, wherein: the controller isconfigured to cause the spatial-mode coupler to change one or morespatial modes in the first subset during transmission through saidspatial-mode coupler of said plurality of modulated optical signals; andthe spatial-mode coupler is configured to couple each of the modulatedoptical signals of said plurality into a corresponding spatial mode ofthe optical link belonging to a currently addressed subset.

In some embodiments of any of the above optical systems, the FEC encoderis configured to employ an FEC code having an FEC block size that causesduration of said transmission of the modulated optical signals carryingthe FEC-encoded block of data to be shorter than a channel coherencetime.

In some embodiments of any of the above optical systems, the datacomprises a pilot data sequence; the optical system is configured tomonitor a performance metric during the transmission through said OMCdevice and the optical link of the optical signal carrying the pilotdata sequence data; and the controller is further configured to selectthe second subset of the spatial modes based on the monitoredperformance metric and configure the OMC device to address the secondsubset of the spatial modes during transmission through said OMC deviceand said optical link of a second optical signal carrying payload data.

In some embodiments of any of the above optical systems, the controlleris further configured to cause the OMC device to keep the second subsetunchanged until a transmission through said OMC device and said opticallink of a third optical signal carrying a pilot data sequence.

In some embodiments of any of the above optical systems, the OMC deviceis a spatial-mode separator of an optical receiver.

In some embodiments of any of the above optical systems, thespatial-mode separator is configured to convert an optical SDM signalreceived from said optical link into a plurality of modulated opticalsignals, each of said modulated optical signals corresponding to arespective spatial mode from a currently addressed subset; and theoptical system further comprises: an O/E converter configured to convertthe plurality of modulated optical signals into a correspondingplurality of streams of digital samples; and a digital signal processorconfigured to process the plurality of streams of digital samples torecover data carried by the optical SDM signal.

In some embodiments of any of the above optical systems, at sortingtimes, the optical receiver is configured to sort the spatial modes ofthe currently addressed subset into a first group and a second groupbased on SNR values of the corresponding modulated optical signals sothat the first group has higher SNR values than the second group; thedigital signal processor is configured to recover the data carried bythe optical SDM signal based on the streams of digital samplescorresponding to the first group of spatial modes; and, between twoconsecutive sorting times, the controller is configured to cause thespatial-mode separator to change one or more spatial modes in the secondgroup of spatial modes while keeping the first group of spatial modesunchanged.

In some embodiments of any of the above optical systems, the controlleris configured to: select a first spatial mode in the second groupcorresponding to a lowest SNR value; randomly select a second spatialmode outside of the currently addressed subset of spatial modes; andcause the spatial-mode separator to address the second spatial modeinstead of the first spatial mode.

In some embodiments of any of the above optical systems, the controlleris configured to: randomly select a first spatial mode from a currentlyaddressed subset; randomly select a second spatial mode outside of thecurrently addressed subset; and cause the OMC device to address thesecond spatial mode instead of the first spatial mode.

According to another embodiment, provided is an optical system having anOMC device configured to address a first subset of spatial modes of anoptical link for carrying data and a second subset of spatial modes ofthe optical link for monitoring a performance metric, wherein the firstsubset and the second subset taken together include all guiding modes ofthe optical link. The optical system also has a controller configured toreconfigure the optical system to change at least one of the first andsecond subsets during transmission of an optical signal carrying datathrough said OMC device and said optical link.

According to yet another embodiment, provided is a method of processingoptical signals. The method comprises the steps of configuring an OMCdevice to address a first subset of spatial modes of an optical link;and changing one or more spatial modes in the first subset whiletransmitting through the OMC device and said optical link an opticalsignal carrying data.

BRIEF DESCRIPTION OF THE DRAWINGS

Other aspects, features, and benefits of various embodiments of theinvention will become more fully apparent, by way of example, from thefollowing detailed description and the accompanying drawings, in which:

FIG. 1 shows a block diagram of an optical MIMO system according to oneembodiment of the disclosure;

FIG. 2 shows representative intensity distributions and polarizationsfor the three lowest linearly polarized (LP) modes of a multimode fiberthat can be used in the system of FIG. 1 according to one embodiment ofthe disclosure;

FIG. 3 shows representative phase/field-strength (PFS) patterns forseveral LP modes of a multimode fiber that can be used in the system ofFIG. 1 according to another embodiment of the disclosure;

FIGS. 4A-4B illustrate an optical mode-coupling (OMC) device that can beused in the system of FIG. 1 according to one embodiment of thedisclosure;

FIGS. 5A-5B illustrate an optical mode mixer that can be used in thesystem of FIG. 1 according to one embodiment of the disclosure;

FIG. 6 shows a cross-sectional side view of an optical mode mixer thatcan be used in the system of FIG. 1 according to another embodiment ofthe disclosure;

FIG. 7 shows a flowchart of a method of operating the system of FIG. 1according to one embodiment of the disclosure;

FIG. 8 shows a flowchart of a method of operating the system of FIG. 1according to another embodiment of the disclosure;

FIG. 9 shows a flowchart of a method of operating the system of FIG. 1according to yet another embodiment of the disclosure;

FIG. 10 shows a flowchart of a method of operating the system of FIG. 1according to yet another embodiment of the disclosure; and

FIG. 11 shows a flowchart of a method of operating the system of FIG. 1according to yet another embodiment of the disclosure.

DETAILED DESCRIPTION

A multimode fiber can provide a higher transmission capacity than asingle-mode fiber, e.g., by means of space-division multiplexing (SDM).More specifically, different guided modes of a multimode fiber can bepopulated with different modulated optical signals or different linearcombinations of a given set of independently modulated optical signals.The original data can then be recovered at the receiver by appropriatelyde-multiplexing and de-convolving the resulting received optical SDMsignal. A similar concept is also applicable to a multi-core fiber.Advantageously, space-division multiplexing can be used to complementother multiplexing techniques, such as time-division multiplexing,wavelength-division multiplexing, orthogonal frequency-divisionmultiplexing, and polarization-division multiplexing, thereby furtherincreasing the accessible transmission capacity of the correspondingoptical-transport link.

As known in the art, a multimode fiber may subject the optical signalstransmitted therethrough to stochastic amplitude fading. The deleteriouseffects of amplitude fading may be mitigated, at least to some extent,by the use of FEC (forward error correction) coding. An FEC code usessystematically generated redundant data to reduce the bit-error rate(BER) at the receiver. The cost of this reduction is a concomitantincrease in the required forward-channel bandwidth, the latter beingcharacterized by the “rate” of the FEC code. In general, a lower-rateFEC code is used for a noisier channel. When the channel conditionsfluctuate over time, the rate and/or the FEC code can be adaptivelychanged to maintain an acceptable BER. However, whenever the channelfluctuations are too fast and/or changing the code rate dynamically istoo complex for a given system, one uses a fixed code rate and a fixedFEC code, which tends to work reliably on most optical-channelinstantiations. However, for those optical-channel instantiations whosemaximum MIMO capacities are lower than the minimum MIMO capacitypermitted by the FEC code, the received SDM signal may becomeun-decodable, which may disadvantageously produce errors for the amountof time the optical channel remains in such a “bad” instantiation,resulting in a system outage.

As used herein, the term “outage” refers to an event during which thereceiver loses its ability to recover data from the received opticalsignals with a BER that is smaller than a specified threshold BER. Ingeneral, at any given time, signal-propagation conditions in afiber-optic link are not uniform for different spatial modes and, inaddition, those conditions can vary over time for each different spatialmode. In an under-addressed optical MIMO system, an outage may occur,for example, when the signal-propagation conditions are particularlyunfavorable for the subset(s) of spatial modes addressed by thetransmitter and/or receiver.

Various embodiments of the disclosure are directed at alleviating atleast some of the above-indicated limitations of FEC coding, as appliedto under-addressed optical MIMO systems. For example, one or more of thedisclosed performance-enhancement techniques may be capable of reducingthe outage probability by changing, from time to time, one or more of(i) the subset of spatial modes addressed by the transmitter, (ii) thesubset of spatial modes addressed by the receiver, and (iii)spatial-mode mixing characteristics of the fiber-optic link. The changesmay be performed in a controllable manner that tends to cause the actualBER to be lower than the BER observed in a corresponding staticconfiguration. Advantageously, the lower BER usually manifests itselfeither as a lower outage probability for a fixed MIMO data-transmissioncapacity or as a higher achievable MIMO data-transmission capacity for aspecified fixed outage probability.

A communications provider may also advantageously use some embodimentsfrom this disclosure to deploy an optical fiber or fiber-optic cablethat is capable of accommodating “future” optical-signal transporttechniques. For example, currently, the optical-transponder technologymay not have reached the point yet that enables all spatial modes to beaddressed. This constraint may in part be due to technical limitationsin the coupling optics and/or limitations in the capabilities of theMIMO-processing ASICs. However, certain embodiments disclosed herein mayenable such a communications provider to deploy a “future-proof” opticalfiber or fiber-optic cable while giving said communications provider ameans for minimizing the outage probability when the correspondingcommunication system remains being operated with the optical fiber orfiber-optic cable being in an “under-addressed” configuration.

FIG. 1 shows a block diagram of an optical MIMO system 100 according toone embodiment of the disclosure. System 100 has an optical transmitter110 and an optical receiver 160 coupled to one another via a fiber-opticlink 140. Fiber-optic link 140 has two fiber-optic sections 146 a-b andan optical mode mixer 150 placed between those two sections. System 100further has a controller 130 that is operatively connected to one ormore of transmitter 110, receiver 160, and mode mixer 150, e.g., asindicated in FIG. 1.

In operation, controller 130 controls, as further described below, theconfigurations of one or more of (i) a spatial-mode (SM) coupler 120 intransmitter 110, (ii) an SM separator 164 in receiver 160, and (iii)optical mode mixer 150. In various embodiments, controller 130 maycomprise one or more separate modules. Some of these separate modules(if any) may be co-located with transmitter 110. Some other modules (ifany) may be co-located with receiver 160. Yet some other modules (ifany) may be placed at one or more dedicated locations along fiber-opticlink 140, e.g., near optical mode mixer 150.

The following alternative embodiments of system 100 are also envisioned.In certain alternative embodiments, at least one of SM coupler 120 andSM separator 164 is a dynamically (re)configurable optical mode-coupling(OMC) device, while mode mixer 150 is either a static optical mode mixeror not present at all. In other alternative embodiments, mode mixer 150is a dynamically (re)configurable device, while one or both of SMcoupler 120 and SM separator 164 are static OMC devices. Furthermore,fiber-optic link 140 may have more than two fiber-optic sections 146with a corresponding instance of optical mode mixer 150 coupled betweenthe respective adjacent fiber-optic sections 146. For example, if link140 has three fiber-optic sections 146, then the link has two opticalmode mixers 150. One of these two optical mode mixers is coupled betweenthe first and second fiber-optic sections of the link, and the other ofthese two optical mode mixers is coupled between the second and thirdfiber-optic sections of the link.

In operation, transmitter 110 receives an input data stream 102 andgenerates an optical SDM output signal 124 that carries the datasupplied by the input data stream. Input data stream 102 is applied toan FEC encoder 112 that adds redundancy to the data, e.g., using asuitable FEC code. Each block of redundant data produced by the FEC codeis optionally interleaved and/or de-multiplexed to produce K paralleldata streams 114 ₁-114 _(K), where K is an integer greater than one. FECencoder 112 then applies data streams 114 ₁-114 _(K) to anelectrical-to-optical (E/O) converter 116.

E/O converter 116 has K optical modulators (not explicitly shown in FIG.1), each configured to generate a corresponding one of modulated opticalsignals 118 ₁-118 _(K). In one embodiment, modulated optical signals 118₁-118 _(K) have the same (common) carrier frequency, and each of theseoptical signals carries the data supplied by the corresponding one ofdata streams 114 ₁-114 _(K). For example, modulated optical signal 118 ₁carries the data supplied by data stream 114 ₁; modulated optical signal118 ₂ carries the data supplied by data stream 114 ₂, etc.

In one embodiment, SM coupler 120 receives optical signals 118 ₁-118_(K) from E/O converter 116 via K respective single-mode fibers andapplies spatial phase filtering to each of these optical signals 118 toproperly condition them for selective coupling into different respectivespatial modes of fiber-optic section 146 a. The spatially phase-filteredsignals (not explicitly shown in FIG. 1) are overlapped in SM coupler120, e.g., as further described below in reference to FIGS. 2-4, togenerate optical SDM signal 124 at an input terminus 144 of fiber-opticsection 146 a.

The spatial phase filtering applied in SM coupler 120 to each of opticalsignals 118 ₁-118 _(K) is such that each of these optical signalscouples substantially into a single selected spatial mode of fiber-opticsection 146 a, with different signals 118 being coupled into differentrespective spatial modes. Depending on the particular embodiment ofsystem 100, the mapping of different optical signals 118 onto differentspatial modes of fiber-optic section 146 a may be static (i.e., fixedand unchanging over time) or dynamic (i.e., changing over time). When SMcoupler 120 is a (re)configurable SM coupler, controller 130 controls,via a control signal 132, the spatial-mode configuration of the SMcoupler and its changes over time.

When an individual optical signal is selectively coupled by SM coupler120 substantially into a single spatial mode of fiber-optic section 146a at input terminus 144 and is thereby transformed into an opticalcomponent of SDM signal 124, which is launched down that fiber-opticsection, it is said that that spatial mode is being “addressed” bytransmitter 110.

In various embodiments, each of fiber-optic sections 146 a-b can beimplemented using, for example (without limitation), one or more of thefollowing: (i) a multimode fiber; (ii) a multi-core fiber; (iii) abundle of single-mode fibers; and (iv) a fiber-optic cable. If amulti-core fiber is used, then each core of that fiber may be designedto support a respective single spatial mode or a respective plurality ofspatial modes. Additional details on possible implementations offiber-optic sections 146 a-b can be found, e.g., in U.S. PatentApplication Publication Nos. 2010/0329670 and 2010/0329671 and in U.S.patent application Ser. No. 13/018,511, all of which are incorporatedherein by reference in their entirety.

In certain embodiments, each of fiber-optic sections 146 a-b supports Nspatial modes, where N>K. In other words, in these embodiments,transmitter 110 addresses fewer spatial modes in fiber-optic link 140than the maximum possible number of spatial modes therein. As a result,fiber-optic link 140 operates as an under-addressed SDM link. In analternative embodiment, N=K. In other alternative embodiments,fiber-optic section 146 a supports N_(a) spatial modes, whilefiber-optic section 146 b supports N_(b) spatial modes, whereN_(a)≠N_(b) and each of N_(a) and N_(b) is greater than or equal to K.

It is known in the art that spatial modes of a multimode or multi-corefiber may undergo inter-mode mixing as they propagate along the lengthof the fiber. As a result, even if a communication signal is completelyconfined to a particular single spatial mode at the input terminus ofthe fiber, other spatial modes will have contributions from thatcommunication signal at the output terminus of the fiber, e.g., anoutput terminus 148 of fiber-optic section 146 a.

Optical mode mixer 150 provides a capability for controllably changingthe spatial-mode mixing characteristics of fiber-optic link 140.Mathematically, the effect of optical mode mixer 150 on the SDM signalpropagating therethrough is described by Eq. (1):

′s_(out)=M′s_(in)  (1)

where ′s_(in) is an input-signal vector having N_(a) components, witheach component representing the optical signal that populates thecorresponding spatial mode addressed by optical mode mixer 150 at outputterminus 148 of fiber-optic section 146 a; ′s_(out) is an output-signalvector having N_(b) components, with each component representing theoptical signal that populates the corresponding spatial mode addressedby optical mode mixer 150 at an input terminus 152 of fiber-opticsection 146 b; and M is an N_(b)×N_(a) matrix that describesspatial-mode mixing characteristics of the optical mode mixer. Ingeneral, each of ′s_(in), ′s_(on), and M is a complex-valued entity. Ina static configuration, mode-mixing matrix M is time-independent and hasconstant matrix elements. In a dynamic configuration, mode-mixing matrixM depends on time and has at least one matrix element that varies overtime. When optical mode mixer 150 is a (re)configurable mode mixer,controller 130 controls, via a control signal 134, the configuration ofthe optical mode mixer and its changes over time.

Receiver 160 receives an optical SDM signal 156 from an output terminus154 of fiber-optic section 146 b, processes this SDM signal, e.g., asfurther described below, to recover the original data of data stream102, and outputs the recovered data via an output data stream 178. SDMsignal 156 is applied to SM separator 164, which splits SDM signal 156into L optical signal components 166 ₁-166 _(L), which are then appliedto an optical-to-electrical (O/E) converter 168. Note that, in variousembodiments, L may or may not equal K. In a representative embodiment, Lmay be smaller than N_(b) and also smaller than N_(a).

In one embodiment, SM separator 164 is an OMC device that is analogousto SM coupler 120, but configured to operate in the reverse direction.For example, SM separator 164 may be designed to couple optical signals166 ₁-166 _(L) into L respective single-mode fibers for delivery to O/Econverter 168. To perform said coupling, SM separator 164 splits SDMsignal 156 into L (e.g., attenuated) copies and applies appropriatespatial phase-filtering to properly condition each of said copies forcoupling into the corresponding one of the single-mode fibers. Thespatial phase-filtering applied in SM separator 164 to the copies of SDMsignal 156 is such that each of the single-mode fibers receives opticalenergy substantially from a single selected spatial mode of fiber-opticsection 146 b, with different single-mode fibers receiving opticalenergy from different respective spatial modes. Depending on theparticular embodiment of system 100, the mapping of different opticalsignals 166 onto different spatial modes of fiber-optic section 146 bmay be static (i.e., fixed and unchanging over time) or dynamic (i.e.,changing over time). When SM separator 164 is a (re)configurable SMseparator, controller 130 controls, via a control signal 136, theconfiguration of the SM separator and its changes over time.

When a single-mode fiber coupled to SM separator 164 receives opticalenergy substantially from a corresponding single selected spatial modeof fiber-optic section 146 b at output terminus 154 and therebygenerates a corresponding one of signals 166 ₁-166 _(L), it is said thatthat spatial mode is being “addressed” by receiver 160.

The relationship between optical signals 118 and optical signals 166 cangenerally be expressed using Eq. (2):

′S_(out)=H′S_(in)  (2)

where ′S_(in) is a vector having K components, wherein each component isa corresponding one of optical signals 118 ₁-118 _(K); ′S_(out) is avector having L components, wherein each component is a correspondingone of optical signals 166 ₁-166 _(L); and H is the L×K channel matrix.Note that channel matrix H depends, among other things, on theconfiguration of SM coupler 120, the configuration of SM separator 164,and the configuration of optical mode mixer 150 (also see Eq. (1)).Different sets of values representing channel matrix H are referred toas different instantiations of that matrix.

In one embodiment, O/E converter 168 performs coherent (homodyne orintradyne) detection of each of optical signals 166 ₁-166 _(L) togenerate a corresponding one of digital electrical signals 170 ₁-170_(L). In each time slot, each of signals 170 ₁-170 _(L) may carry twovalues: one corresponding to the in-phase (I) component of thecorresponding one of optical signals 166 ₁-166 _(L) and the othercorresponding to the quadrature-phase (Q) component of that opticalsignal. Various optical detectors that can be used to implement O/Econverter 168 are disclosed, e.g., in U.S. Patent ApplicationPublication Nos. 2010/0158521 and 2011/0038631, and International PatentApplication No. PCT/US09/37746 (filed on Mar. 20, 2009), all of whichare incorporated herein by reference in their entirety.

A digital signal processor (DSP) 172 processes digital electricalsignals 170 ₁-170 _(L) and, based on said processing, generates outputdata stream 178. The processing includes, but is not limited to, (i)de-convolving signals 170 ₁-170 _(L) to generate a set of recovered datastreams (not explicitly shown in FIG. 1), wherein each recovered datastream carries data corresponding to one of data streams 114 ₁-114 _(K);(ii) de-interleaving blocks of data carried by the recovered datastreams if FEC encoder 112 in transmitter 100 is configured tointerleave the FEC-encoded data in the process of generating datastreams 114 ₁-114 _(K); (iii) multiplexing the de-interleaved data or,if no de-interleaving needs to be performed, directly the blocks of datacarried by the recovered data streams to generate an estimated datastream (not explicitly shown in FIG. 1); and (iv) FEC-decoding theestimated data stream to generate output data stream 178. Provided thatthe FEC code is sufficiently robust for the particular transmissioncharacteristics/conditions of link 140, most (if not all) of thetransmission/decoding errors are corrected, and output data stream 178approximates (if not matches) input data stream 102 with a BER that issmaller than the maximum acceptable BER value specified for system 100.

In general, to properly perform the de-convolving step of theabove-described signal processing, DSP 172 needs to receive, via signals170 ₁-170 _(L), a sufficient number of signal samples. For example, todecode Q optical symbols carried by SDM signal 156, DSP 172 needs toobtain at least Q independent samples of that signal. The signalprocessing applied to these samples is generally based onmatrix-diagonalization algorithms aimed at reversing the effects ofspatial-mode mixing in fiber-optic link 140, including the effects ofspatial-mode mixing imposed by optical mode mixer 150 (also see Eq.(1)).

For illustration purposes, the representative embodiments describedbelow correspond to an embodiment of system 100 in which each offiber-optic sections 146 a and 146 b is a multimode fiber. From theprovided description, one of ordinary skill in the art will be able tomodify the described embodiments to adapt them for an embodiment ofsystem 100 in which, for example, (i) each of fiber-optic sections 146 aand 146 b is a multi-core fiber or (ii) one of fiber-optic sections 146a and 146 b is a multi-core fiber while the other fiber-optic section isa multimode fiber.

In general, a multimode fiber has two broad classes of spatial modes:radiation modes and guided modes. Radiation modes carry energy out ofthe fiber core, which is then quickly dissipated. Radiation modes arenot of interest for this disclosure and, as such, are not discussedhere. Guided modes are primarily confined to the fiber core, andpropagate energy along the fiber, thereby transporting information andpower along fiber-optic link 140. Each guided mode has its own distinctvelocity and can be further decomposed into two orthogonally polarizedcomponents. Any electro-magnetic (EM) field distribution within theoptical fiber can generally be expressed as a combination of guidedmodes.

For a given wavelength λ, a multimode fiber of fiber section 146, cansupport multiple guided modes if the normalized frequency parameter V(also referred to as the V number) is greater than 2.405. Eq. (3) givesthe expression for V:

$\begin{matrix}{V = {\frac{2\pi \; a}{\lambda}{NA}}} & (3)\end{matrix}$

where α is the fiber-core radius, and NA is the numerical aperture. Fora step-index fiber, the numerical aperture is given by Eq. (4):

NA=√{square root over (n₁ ² −n ₂ ²)}  (4)

where n₁ is the refractive index of the fiber core, and n₂ is therefractive index of the fiber cladding.

The guided modes can generally be classified as (i) transverse electric(TE) modes, for which the axial component of the electric field is zero;(ii) transverse magnetic (TM) modes, for which the axial component ofthe magnetic field is zero; and (iii) HE or EH modes, for which neitherthe axial component of the electric field nor the axial component of themagnetic field is zero. The designation of HE or EH depends on which ofthe electric (E) and magnetic (H) field components is dominant.

The guided modes of a multimode fiber can be ordered based on one ormore of the following: (i) the number of intensity lobes in thetransverse plane, (ii) group velocity, and (iii) the magnitude of thelongitudinal wavevector. The lowest-order (a.k.a. fundamental) modetypically has a single intensity lobe, the highest group velocity, andthe largest longitudinal wavevector. The remaining (higher-order) modesare typically ordered based on the magnitude of their longitudinalwavevectors. For some waveguide cross-sections and V numbers, inaddition to the use of the magnitude of longitudinal wavevectors, one ofthe remaining two criteria may need to be invoked to determine therelative order of some guided modes.

The refractive-index profiles of most step-index optical fibers used incommunication links, such as fiber-optic link 140, have a relativelysmall (e.g., smaller than about 0.05) contrast Δ, which makes thesefibers only weakly guiding. Eq. (5) gives the definition of Δ for astep-index fiber:

$\begin{matrix}{\Delta = \frac{n_{1} - n_{2}}{n_{1}}} & (5)\end{matrix}$

In the approximation of weak guidance for generally cylindrical fibers,the TE, TM, HE, and EH guided modes become the modes that are referredto as the linearly polarized (LP) modes.

The following notation is usually adhered to in the description of theLP modes. Each LP mode is designated using two integer indices, e.g., inthe form of subscripts: LP_(jk). The first integer index (j) gives thenumber of 2π-sized phase increments in the electric field per oneazimuthal rotation about the fiber axis (e.g., the Z-coordinate axis).The second integer index (k) gives the number of electric-field nodes inthe radial dimension, with the zero field at the outer edge of the fielddistribution counted as a radial node. Some of the LP modes are alsogiven a designating letter, e.g., a, b. The letter follows the twointeger indices and is used to distinguish certain degenerate modes. Inaddition, each LP mode can have two different polarizations, e.g., an Xpolarization and a Y polarization, where X and Y are the two transverse(i.e., orthogonal to the fiber axis) coordinate axes.

FIG. 2 graphically shows representative intensity distributions andpolarizations for the three lowest LP modes of a multimode fiber thatcan be used in link 104 according to one embodiment of the disclosure.The intensity distributions are color-coded so that (i) the dark blue(outer) color corresponds to the zero intensity, (ii) the dark red(inner) color corresponds to the highest intensity, and (iii) the colorsin between correspond to the intermediate intensities in therainbow-like progression from blue to red. The dotted arrows indicatethe respective electric-field polarizations for different modes. Each ofthe shown LP modes is doubly degenerate, with the same intensitydistribution corresponding to each of two orthogonal (e.g., X and Y)polarizations.

The fundamental mode (LP₀₁) has an intensity profile that is similar tothat of a Gaussian beam. The LP₀₁ mode corresponds to the HE₁₁ mode of astrongly guiding fiber.

The next lowest-order mode (LP₁₁) has an intensity profile comprisingtwo intensity peaks characterized by a phase difference of 180 degreesbetween the corresponding electric fields. In the LP_(11a) mode, theintensity peaks are lined up along the X-axis. In the LP_(11b) mode, theintensity peaks are similarly lined up along the Y-axis. The differentdegenerate states of the LP_(11a) and LP_(11b) modes correspond todifferent linear combinations of the TE₀₁, TM₀₁, and HE₂₁ modes of astrongly guiding fiber. If the V number (see Eq. (3)) is in the rangebetween about 2.405 and about 3.9, then the LP₀₁, LP_(11a), and LP_(11b)modes are typically the only guided modes supported by the fiber.

FIG. 3 graphically shows representative phase/field-strength (PFS)patterns for several LP modes of a multimode fiber that can be used infiber-optic link 140 according to another embodiment of the disclosure.Each PFS pattern is color-coded using a color scheme in which: (i) thedegree of color saturation represents the optical-field strength and(ii) the color itself represents the phase of the electric field. Forexample, the light red color corresponds to lower optical-field strengththan the dark red color. A rainbow-like change in color from blue to redrepresents a continuous change in the relative phase from −π to +π.

PFS patterns for different states of degenerate LP modes can be obtainedby appropriately rotating the PFS patterns shown in FIG. 3. For example,the PFS pattern for the LP_(11b) mode (see FIG. 2) can be obtained byrotating by 90 degrees the PFS pattern shown in the second-from-the-leftpanel in the top row of FIG. 3. The intensity distribution for the LPmode can be obtained by calculating a square of the absolute values ofthe corresponding PFS pattern. For example, the intensity distributionfor the LP₀₁ mode shown in the left-most panel of FIG. 2 can be obtainedby calculating a square of the absolute values of the PFS pattern shownin the left-most panel in the top row of FIG. 3. Similarly, theintensity distribution for the LP_(11a) mode shown in thethird-from-the-left panel of FIG. 2 can be obtained by calculating asquare of the absolute values of the PFS pattern shown in thesecond-from-the-left panel in the top row of FIG. 3.

To efficiently and selectively couple light into a particular LP mode ofa multimode fiber, the PFS pattern and polarization created by a lightsource at an end facet of the fiber should approximate closely the PFSpattern and polarization of that LP mode. In particular, the light thatdoes not match the appropriate PFS pattern and polarization may becoupled into a different LP mode, be coupled into a radiation mode,and/or be reflected back from the end facet of the multimode fiber. Forexample, to efficiently and selectively couple light into theX-polarized LP_(11a) mode, the corresponding light source should beconfigured to create a PFS pattern that closely approximates the PFSpattern shown in the second-from-the-left panel in the top row of FIG. 3and the polarization shown in the third-from-the-left panel of FIG. 2.

For brevity and clarity reasons, the description below refers tolow-order LP modes. However, embodiments of the disclosure disclosedherein are not so limited. For example, the illustrated inventiveconcepts are similarly applicable to a strongly guiding multimode fiberwhose guided modes are the corresponding TE, TM, HE, and EH modes,rather than the LP modes illustrated in FIGS. 2 and 3. The illustratedinventive concepts are also applicable to the “supermodes” of a coupledmulti-core fiber, a representative description of which can be found,e.g., in a post-deadline paper published in the proceedings of the 2011European Conference on Optical Communication (ECOC) by R. Ryf, A.Sierra, R.-J. Essiambre, et al., entitled “Coherent 1200-km 6×6 MIMOMode-Multiplexed Transmission over 3-core Microstructured Fiber,” whichis incorporated herein by reference in its entirety.

FIGS. 4A-4B illustrate an OMC device 400 that can be used as SM coupler120 in transmitter 110 and/or SM separator 164 in receiver 160 accordingto one embodiment of the system 100 (also see FIG. 1). Morespecifically, FIG. 4A shows a block diagram of OMC device 400. FIG. 4Bshows spatial-phase patterns that can be used in spatial-phase filters420 of OMC device 400. For clarity of depiction, OMC device 400 is shownas having two spatial-mode channels. However, from the provideddescription, one of ordinary skill in the art will understand how todesign an OMC device having any suitable number of channels for use insystem 100. For example, a new optical channel can be created by addinga set of optical elements similar to that used to add Channel 2 toChannel 1 in OMC device 400.

In various embodiments, spatial-phase filters 420 can be static phasemasks or dynamically (re)configurable devices capable of changing thedisplayed spatial-phase patterns under external control, e.g., effectedby control signal 132 or 136 (see FIG. 1).

OMC device 400 is shown in FIG. 4A as being coupled to single-modefibers 402 ₁-402 ₂ at the left side thereof and to a multimode fiber 406at the right side thereof. When OMC device 400 is used as SM coupler 120in transmitter 110 (see FIG. 1), each of single-mode fibers 402 ₁-402 ₂is configured to receive a corresponding one of modulated opticalsignals 118, and multimode fiber 406 is a part of fiber section 146 a.When OMC device 400 is used as SM separator 164 in receiver 160 (seeFIG. 1), each of single-mode fibers 402 ₁-402 ₂ is configured to carry acorresponding one of optical signal components 166, and multimode fiber406 is a part of fiber section 146 b.

For illustration purposes, the description of OMC device 400 providedbelow assumes that light is being directed from single-mode fibers 402₁-402 ₂ to multimode fiber 406, e.g., as in the configurationcorresponding to SM coupler 120 (FIG. 1). From this description, one ofordinary skill in the art will understand how OMC device 400 operateswhen light is being directed from multimode fiber 406 to single-modefibers 402 ₁-402 ₂, e.g., as in the configuration corresponding to SMseparator 164 (FIG. 1).

OMC device 400 has two lenses 410, each of which collimates a respectivediverging light beam applied to the OMC device by a respective one offibers 402. Each of the resulting collimated beams passes through arespective one of spatial-phase filters 420 to create a correspondingphase-filtered beam 422. A plurality of mirrors 430 then spatiallysuperimpose the two phase-filtered beams 422 and direct a resulting“superimposed” beam 432 toward fiber 406. Note that mirror 430 ₄ is apartially transparent mirror, while each of mirrors 430 ₁-430 ₃ is aregular, non-transparent mirror. Two lenses 442 and 446 and an aperture444 are used to compress (e.g., reduce the size of) and spatially filterbeam 432 to produce an output beam 452 that impinges on an inputterminus 454 of multimode fiber 406 and creates an intendedsuperposition of PFS patterns corresponding to the selected spatialmodes of the multimode fiber (also see FIGS. 2-3).

Depending on the spatial modes assigned to the two spatial-mode channelsof OMC device 400, the spatial-phase patterns displayed by spatial-phasefilters 420 ₁ and 420 ₂ are appropriately chosen, e.g., from the set ofspatial-phase patterns shown in FIG. 4B. For example, if a particularspatial-mode channel of OMC device 400 is assigned the LP_(11a) mode offiber 406, then the appropriately oriented spatial-phase pattern labeledLP11 in FIG. 4B is displayed by the corresponding spatial-phase filter420 in that spatial-mode channel. Similarly, if a particularspatial-mode channel of OMC device 400 is assigned the LP_(21b) mode offiber 406, then the appropriately oriented spatial-phase pattern labeledLP21 in FIG. 4B is displayed by the corresponding spatial-phase filter420 in that spatial-mode channel, and so on. The combined effect of thespatial-phase filtering imposed by the corresponding filter 420 and thespatial filtering imposed by aperture 444 is that the optical channelcreates at input terminus 454 of fiber 406 an intended PFS patterncorresponding to the selected spatial mode, thereby efficiently couplingthe optical signal received via the corresponding single-mode fiber 402into that spatial mode of multimode fiber 406.

Note that some of the spatial phase patterns shown in FIG. 4B are binaryphase patterns (i.e., phase patterns that can locally impose only one oftwo possible phase shifts, e.g., either 0 or π). In particular, phasepatterns corresponding to the LP01, LP02, and LP03 modes are binaryphase patterns. The remaining phase patterns shown in FIG. 4B are“analog” phase patterns because different portions of the pattern canimpose phase shifts selected from a continuous phase-shift range. Analogphase patterns are shown in FIG. 4B using a color scheme, in which: (i)different colors represent different phase shifts in a continuous 2πinterval and (ii) for some phase patterns, different bands of the samecolor represent phase shifts that differ from each other by an integermultiple of 2π.

In one embodiment, OMC device 400 might employ a single, relativelylarge, continuous spatial-phase filter in place of two separate filters420 ₁ and 420 ₂. This relatively large, continuous filter may beconfigured to display in its different sections (portions), two or morespatial-phase patterns from FIG. 4B. These different sections can bearranged so that one section serves as spatial-phase filter 420 ₁ andanother section serves as spatial-phase filter 420 ₂.

Various additional OMC devices that can be used to implement SM coupler120 and/or SM separator 164 (see FIG. 1) are disclosed, e.g., in theabove-cited U.S. Patent Application Publication Nos. 2010/0329670 and2010/0329671 and, also, in U.S. Patent Application Publication No.2011/0243490 and U.S. patent application Ser. No. 12/986,468, both ofwhich are incorporated herein by reference in their entirety.

FIGS. 5A-5B illustrate an optical mode mixer 500 that can be used asoptical mode mixer 150 (FIG. 1) according to one embodiment of system100. More specifically, FIG. 5A shows an overall block diagram of modemixer 500. FIG. 5B shows a schematic diagram of a 2×2 optical mixer 520,a plurality of which are used in mode mixer 500.

Referring to FIG. 5A, mode mixer 500 is coupled between multimode fibers546 a and 546 b. In a representative configuration, multimode fiber 546a may be used to implement fiber-optic section 146 a, and multimodefiber 546 b may be used to implement fiber-optic section 146 b (see FIG.1). Optical mode mixer 500 comprises (i) OMC devices 510 a and 510 bcoupled to multimode fibers 546 a and 546 b, respectively, and (ii) aninterconnected array 530 of 2×2 optical mixers 520 coupled between theseOMC devices as indicated in FIG. 5A. In one embodiment, each of OMCdevices 510 a and 510 b may be analogous to OMC device 400 (FIG. 4) wereit implemented for four instead of just two single-mode fibers 402.

Mixer array 530 is configured to (i) receive optical signals 512 ₁-512 ₄generated by OMC device 510 a, (ii) optically mix the received signalsto generate optical signals 532 ₁-532 ₄, and (iii) apply the lattersignals to OMC device 510 b. As a result, mixer array 530 can be used toimplement Eq. (1) with a (4×4) matrix M. The individual matrix elementsof matrix M depend on the states of mixers 520, with the latter beingcontrolled by control signals 542 ₁-542 ₆ generated by a mixercontroller 540. Therefore, matrix M can be varied as a function of timeby configuring mixer controller 540 to change the state(s) of one ormore mixers 520. Mixer controller 540 may be configured to generatecontrol signals 542 ₁-542 ₆ based on an external control signal, such ascontrol signal 134 (FIG. 1). Alternatively, mixer controller 540 may besaid to be part of controller 130, in which case control signal 134 maybe said to comprise control signals 542 ₁-542 ₆.

Referring to FIG. 5B, an individual optical mixer 520 comprises aMach-Zehnder interferometer having a first arm 526 a and a second arm526 b, with both arms coupled between two (e.g., 3-dB) optical couplers522. Arm 526 b includes a phase shifter (PS) 524 that receives acorresponding control signal 542 from controller 540. Each of outputsignals S₃ and S₄ produced by mixer 520 represents a linear combinationof input signals S₁ and S₂ applied to the mixer, with the coefficientsof the linear combination depending on (i) the wavelength of signals S₁and S₂, (ii) the length difference (if any) between arms 526 a and 526b, and (iii) the value of the phase shift imposed by phase shifter 524.The coefficients can be changed, as appropriate or necessary, bychanging the value of the phase shift imposed by phase shifter 522.

Although array 530 is illustratively shown as having six mixers 520interconnected in the manner indicated in FIG. 5A, other arrays maysimilarly be used. More specifically, the topology and/or size of array530 may be selected, e.g., based on the values of N_(a), N_(b), L, and Kspecified for system 100. For example, if N_(a)>N_(b), then some of theoutput lines analogous to output lines 532 _(i) may not be connected tothe corresponding OMC device analogous to OMC device 510 b. IfN_(a)<N_(b), then some of the output lines analogous to output lines 532_(i) may need to be divided before being coupled into the correspondingports the OMC device analogous to OMC device 510 b.

Although exemplary embodiments of optical mode mixer 500 have beendescribed as being based on optical mixers 520 of Mach-Zehnder type,other types of optical mixers or switches can similarly be used. Forexample, configurable switches/mixers having one or more than two inputports can be used to form a corresponding switch/mixer array analogousto array 530. Similarly, configurable switches/mixers having one or morethan two output ports can also be used. One or both of OMC devices 510a-b may optionally be configurable, e.g., similar to SM coupler 120and/or SM separator 164 (FIG. 1). The corresponding control signals areindicated in FIG. 5A using the dashed lines and labeled 534 a and 534 b.In alternative embodiments, OMC devices that are designed to addressmore or fewer than four spatial modes of the corresponding multimodefiber or fiber-optic cable may be used instead of OMC devices 510 a-b.The OMC device located at the ingress (left) side of optical mode mixer500 may be configured to address a different number of spatial modesthan the OMC device located at the egress (right) side of the opticalmode mixer.

FIG. 6 shows a cross-sectional side view of an optical mode mixer 600that can be used as optical mode mixer 150 according to anotherembodiment of system 100. Optical mode mixer 600 is coupled betweenmultimode fiber sections 646 a and 646 b. In a representativeconfiguration, multimode fiber section 646 a may be used to implementfiber-optic section 146 a, and multimode fiber section 646 b may be usedto implement fiber-optic section 146 b (see FIG. 1).

Optical mode mixer 600 has a mechanical (e.g., piezoelectric) actuator630 arranged to press plates 620 a-b against a section 610 of the fiberthat is sandwiched between them. The force with which actuator 630pushes on plates 620 a-b is controlled by an external control signal,such as control signal 134 (see FIG. 1). Each of plates 620 a-b has arespective uneven surface 612 that is in direct physical contact withfiber section 610. In one embodiment, surface 612 may be corrugatedand/or have a relatively rough surface finish. When actuator 630 pressestwo uneven surfaces against fiber section 610, the fiber ismicro-deformed, which causes relatively strong spatial-mode crosstalkand/or scrambling to occur in that fiber section. The type and/or extentof this spatial-mode crosstalk and/or scrambling depend on the magnitudeof the mechanical force applied by actuator 630. In general, differentmechanical deformations of the fiber produce different types and/orextents of spatial-mode crosstalk/scrambling in fiber section 610. Thisphenomenon, in turn, manifests itself as different spatial-mode mixingcharacteristics for mode mixer 600, e.g., as mathematically expressed bydifferent matrices M in Eq. (1). Matrix M can therefore be varied as afunction of time by configuring actuator 630 to vary the mechanicalforce that it applies to plates 620 a-620 b.

In one embodiment, optical mode mixer 600 may be implemented using anautomated version of the fiber-mode scrambler that is commerciallyavailable from Newport Corporation of Irvine, Calif., e.g., as ModelFM-1.

Referring back to FIG. 1, the operation of system 100 can becharacterized by at least three different time constants: t_(s),T_(FEC), and τ_(c). More specifically, time constant t_(s) is theduration of a signaling interval, e.g., the time period allocated to oneconstellation symbol in an individual optical signal 118. Period t_(s)is inversely proportional to the bit rate. Time constant T_(FEC)represents a maximum possible time duration for which a burst of errorsmay occur, with the operative FEC code still being able to correct theerrors. The maximum amount of errors that the FEC code can correct isalso referred to as the code's error correction capacity. The code'serror correction capacity depends on the FEC block size, thepost-encoding FEC scrambling depth, and the nature of the underlyingalgorithm(s). Time constant τ_(c) is the channel coherence time, whichis a measure of the minimum time required for a magnitude change inoptical signal 156 induced by multi-path fading in fiber-optic link 140to become uncorrelated from its previous value (when the configurationsof SM coupler 120 and optical mode mixer 150 are static).

An outage in system 100 may, for example, be caused by a “deep fade” ofone or more signal components of optical signal 156, which maytemporarily render optical signals 166 un-decodable due to a temporarybreakdown in FEC-decoding processing performed by DSP 172. A deep fadeof a signal component may be caused, e.g., by strong destructiveinterference experienced by that signal component at receiver 160 due toan unfavorable instantiation of channel matrix H (see Eq. (2)). When thecumulative effect of one or more deep fades that occur duringtransmission of an FEC-encoded block of data is such that a sufficientlylarge number of symbols in optical signals 166 have an insufficientoptical signal-to-noise ratio (SNR) to be decoded correctly, theFEC-decoding processing breaks down, thereby causing an outage. Such abreakdown may occur, for example, when a deep fade lasts a relativelylong period of time so that the corresponding errors exceed the code'serror correction capacity. This may occur, e.g., if τ_(c)>T_(FEC).

Mathematically, fading can usually be modeled as a time-varying randomprocess. The typical (e.g., average) duration of a deep fade can beexpressed using channel coherence time τ_(c), with different modalcomponents of optical signal 156 generally experiencing their respectivedeep fades in a statistically random manner. The random nature of fadingcauses some time intervals to have a relatively large number of signalcomponents in deep fades and some other time intervals to have arelatively small number of signal components in deep fades. One ofordinary skill in the art will appreciate that a system outage is morelikely to occur during one of the former time intervals than during oneof the latter time intervals.

The methods of operating system 100 disclosed herein below are directedat reducing the frequency of temporary breakdowns in the FEC-decodingprocessing, e.g., by reducing the number of time intervals having arelatively large number of signal components in deep fades. In variousembodiments, this reduction is achieved at the cost of (i) reducing thenumber of time intervals having a relatively small number of signalcomponents in deep fades and/or (ii) using a portion of the bandwidthfor monitoring the occurrence of deep fades rather than for transmittingpayload data. A representative method of operating system 100 accordingto one embodiment may include one or more of: (i) changing theconfiguration of SM coupler 120, (ii) changing the configuration of SMseparator 164, and (iii) changing the configuration of optical modemixer 150.

FIG. 7 shows a flowchart of a method 700 of operating system 100according to one embodiment of the disclosure. Method 700 may beimplemented using transmitter 110 or receiver 160. Exemplary steps ofmethod 700 are described below in reference to both FIG. 1 and FIG. 7.

At step 702 of method 700, controller 130 selects a subset of spatialmodes to be addressed by the pertinent OMC device (e.g., SM coupler 120or SM separator 164). For example, if method 700 is implemented usingtransmitter 110, then the selected subset consists of K spatial modes offiber 146 a, and there are

$\frac{N_{a}!}{{K!}{\left( {N_{a} - K} \right)!}}$

different possible subsets from which this subset can be chosen, where !indicates the factorial notation. If method 700 is implemented usingreceiver 160, then the selected subset consists of L spatial modes offiber 146 b, and there are

$\frac{N_{b}!}{{L!}{\left( {N_{b} - L} \right)!}}$

different possible subsets from which this subset can be chosen.Controller 130 may employ any suitable algorithm for selecting a subsetof spatial modes from the plurality of different possible subsets. Forexample, in one implementation of method 700, controller 130 may beconfigured to select a subset of spatial modes from the plurality ofdifferent possible subsets in a random manner. In anotherimplementation, controller 130 may be configured to select a set ofspatial modes from the plurality of different possible sets in around-robin manner. In yet another implementation, controller 130 may beconfigured to select a set of spatial modes from the plurality ofdifferent possible sets by putting preference on certain modes that areknown to result in less fading in the optical link due to the specificsof the employed fiber design(s). In yet another implementation,controller 130 may be configured to select a set of spatial modes fromthe plurality of different possible sets by choosing the modes that areeither weakly or strongly coupled to each other, depending on theemployed fiber design(s).

At step 704, controller 130 generates an appropriate control signal toconfigure the pertinent OMC device to use a set of phase filters (e.g.,analogous to phase filters 420 ₁-420 ₂, FIG. 4A) corresponding to thesubset of spatial modes selected at step 702. For example, if theoperative spatial modes are LP modes, then the phase filters used in theOMC device may have phase patterns appropriately selected from the phasepatterns shown in FIG. 4B.

If method 700 is implemented using transmitter 110, then controller 130generates control signal 132, which appropriately configures SM coupler120 in step 704. If method 700 is implemented using receiver 160, thencontroller 130 generates control signal 136, which appropriatelyconfigures SM separator 164 in step 704.

The control signal (132 or 136) is generated so that it causes theconfiguration of the pertinent OMC device to remain static for aspecified period of time (t_(hold)). In a representative embodiment,time t_(hold) is selected to be significantly smaller than channelcoherence time τ_(c), and also significantly smaller than time T_(FEC).After time t_(hold) has passed, the processing of method 700 is directedfrom step 704 back to step 702.

In various embodiments of method 700, steps 702 and 704 may be performedeither asynchronously or synchronously with respect to the transmissionof FEC-encoded blocks of data. Data-recovery algorithms executed by DSP172 are made aware of the timing of steps 702 and 704 and perform thecorresponding data processing accordingly.

In a representative embodiment, method 700 is implemented to cyclethrough steps 702 and 704 at a relatively high repetition rate, e.g.,causing a relatively large number of cycles to be executed duringtransmission of one FEC-encoded block of data. This relatively fastcycling through steps 702 and 704 enables receiver 160 to be exposed toboth favorable and unfavorable instantiations of channel matrix H (seeEq. (2)) during said transmission. Provided that the operative FEC codehas sufficient error-correcting capacity for the corresponding averageinstantiation of channel matrix H, the FEC-decoding processingimplemented in DSP 172 is typically capable of correcting the bursterrors caused by the unfavorable instantiations of channel matrix H,which instantiations tend to be relatively short-lived due to therelatively fast cycling through steps 702-704. In contrast, without therelatively fast changes of channel matrix H imposed by method 700, anunfavorable instantiation of channel matrix H may last for a relativelylong period of time, which may cause the FEC-decoding processing of thecorresponding block of data to break down due to insufficienterror-correcting capacity of the FEC code.

FIG. 8 shows a flowchart of a method 800 of operating system 100according to another embodiment of the disclosure. Similar to method 700(FIG. 7), method 800 may be implemented using the OMC device oftransmitter 110 or receiver 160. Exemplary steps of method 800 aredescribed below in reference to FIGS. 1, 7, and 8.

At step 802, controller 130 configures transmitter 110 and receiver 160to enter a training mode. During the training mode, transmitter 110 isconfigured to transmit optical signals carrying one or more pilot-datasequences, and receiver 160 is configured to monitor the BER or othersuitable performance metric corresponding to this transmission.

At step 804, controller 130 configures transmitter 110 or receiver 160to perform method 700 (FIG. 7), while transmitter 110 is transmittingpilot-data sequences, and receiver 160 is monitoring a performancemetric (e.g., the BER) corresponding to this transmission.

At step 806, DSP 172 identifies one or more time intervals correspondingto favorable performance-metric values (e.g., the minimum BER value)observed during step 804. DSP 172 then uses a feedback signal 174 tocommunicate this information to controller 130. Based on the receivedinformation, controller 130 identifies the corresponding one or morespatial-mode configurations of (e.g., one or more sets of phase filtersused in) the pertinent OMC device. For example, if method 800 isimplemented using SM coupler 120, then controller 130 identifies the oneor more spatial-mode configurations of the SM coupler corresponding tosaid one or more time intervals of favorable performance-metric valuesobserved during step 804. Alternatively, if method 800 is implementedusing SM separator 160, then controller 130 identifies the one or morespatial-mode configurations of the SM separator corresponding to saidone or more time intervals of favorable performance-metric valuesobserved during step 804.

At step 808, controller 130 selects one configuration from the one ormore spatial-mode configurations identified at step 806. Then, using anappropriate control signal (e.g., control signal 132 or 136), controller130 configures the pertinent OMC device to use the selected spatial-modeconfiguration so that said configuration is being held static for theentire duration of step 810. As already indicated above, the pertinentOMC device may be SM coupler 120 or SM separator 164.

At step 810, controller 130 configures transmitter 110 and receiver 160to operate in a payload-transmission mode for a specified period oftime. During the payload-transmission mode, transmitter 110 isconfigured to transmit optical signals carrying payload data, andreceiver 160 is configured to demodulate and decode the correspondingreceived signals to recover said payload data. Since the configurationselected at step 808 corresponds to a favorable instantiation of channelmatrix H, the FEC-decoding processing in DSP 172 is likely to havesufficient error-correcting capacity to correct possible errors and toavoid a system outage during step 810.

In a representative implementation, the duration of step 810 is selectedto be on the order of or slightly smaller than channel coherence timeτ_(c). One of ordinary skill in the art will understand that thisduration is likely to ensure that relatively favorable channelconditions can persist for the entire duration of step 810. After theperiod of time allocated to step 810 has passed, the processing ofmethod 800 is directed from step 810 back to step 802.

One of ordinary skill in the art will appreciate that method 800 maybeneficially be used in system 100, e.g., when fiber-optic link 140 hasa relatively large value of channel coherence time τ_(c). The lattercharacteristic advantageously enables system 100 to spend a relativelysmall fraction of time in the training mode while being able to transmita relatively large number of blocks of FEC-encoded payload data duringeach occurrence of step 810.

FIG. 9 shows a flowchart of a method 900 of operating system 100according to yet another embodiment of the disclosure. Method 900 may beimplemented using optical mode mixer 150 (FIG. 1). Exemplary steps ofmethod 900 are described below in reference to FIGS. 1, 5, 6, and 9.

At step 902 of method 900, controller 130 selects an implementable setof values, each corresponding to a respective matrix element ofmode-mixing matrix M (see Eq. (1)). Controller 130 may employ anysuitable algorithm for selecting this implementable set of values. Forexample, in one implementation of method 900, controller 130 may beconfigured to randomly select this set from a list of pre-computed setsstored in a memory.

At step 904, based on the values selected at step 902, controller 130generates control signal 134 that configures optical mode mixer 150 toadopt a configuration that implements the spatial-mode mixingcorresponding to said selected values. For example, in one embodiment,control signal 134 may be used to configure mixer controller 540 togenerate an appropriate set of control signals 542 for mixer array 530(see FIG. 5). In another embodiment, control signal 134 may be used tospecify the force to be applied by actuator 630 to plates 620 a-b (seeFIG. 6).

Control signal 134 is generated so that it causes the configuration ofoptical mode mixer 150 to remain static for a specified period of time(t_(hold)). In a representative embodiment, time t_(hold) is selected tobe significantly smaller than channel coherence time τ_(c), and alsosignificantly smaller than time T_(FEC). After time t_(hold) has passed,the processing of method 900 is directed from step 904 back to step 902.

In various embodiments of method 900, steps 902 and 904 may be performedeither asynchronously or synchronously with respect to the transmissionof FEC-encoded blocks of data. Data-recovery algorithms executed by DSP172 are made aware of the timing of steps 902 and 904 and perform thecorresponding data processing accordingly.

In a representative embodiment, method 900 is implemented to cyclethrough steps 902 and 904 at a relatively high repetition rate, e.g.,causing a relatively large number of cycles to be executed duringtransmission of one FEC-encoded block of data. This relatively fastcycling through steps 902 and 904 may reduce the outage probability forthe reasons similar to those already indicated above in reference tomethod 700 (FIG. 7).

FIG. 10 shows a flowchart of a method 1000 of operating system 100according to yet another embodiment of the disclosure. Method 1000 maybe implemented using optical mode mixer 150. Exemplary steps of method1000 are described below in reference to FIGS. 1, 9, and 10.

At step 1002, controller 130 configures transmitter 110 and receiver 160to enter a training mode. During the training mode, transmitter 110 isconfigured to transmit optical signals carrying one or more pilot-datasequences, and receiver 160 is configured to monitor a suitableperformance metric (e.g., the BER) corresponding to this transmission.

At step 1004, controller 130 configures optical mode mixer 150 toperform method 900 (FIG. 9), while transmitter 110 is transmittingpilot-data sequences, and receiver 160 is monitoring the performancemetric corresponding to this transmission.

At step 1006, DSP 172 identifies one or more time intervalscorresponding to favorable performance-metric values (e.g., the minimumBER value) observed during step 1004. DSP 172 then uses feedback signal174 to communicate this information to controller 130. Based on thereceived information, controller 130 identifies the corresponding one ormore spatial-mode mixing configurations of (e.g., one or more sets ofimplementable values for mode-mixing matrix M to be implemented by)optical mode mixer 150.

At step 1008, controller 130 selects one configuration from the one ormore spatial-mode mixing configurations identified at step 1006. Then,using control signal 134, controller 130 configures optical mode mixer150 to adopt the selected configuration so that said configuration isbeing held static for the entire duration of step 1010.

At step 1010, controller 130 configures transmitter 110 and receiver 160to operate in a payload-transmission mode for a specified period oftime. During the payload-transmission mode, transmitter 110 isconfigured to transmit optical signals carrying payload data, andreceiver 160 is configured to demodulate and decode the correspondingreceived signals to recover said payload data. Since the configurationselected at step 1008 corresponds to a favorable instantiation ofchannel matrix H, the FEC-decoding processing in DSP 172 is likely tohave sufficient error-correcting capacity to correct possible errors andto avoid a system outage during step 1010.

In a representative implementation, the duration of step 1010 isselected to be on the order of or slightly smaller than channelcoherence time τ_(c). One of ordinary skill in the art will understandthat this duration is likely to ensure that relatively favorable channelconditions can persist for the entire duration of step 1010. After theperiod of time allocated to step 1010 has passed, the processing ofmethod 1000 is directed from step 1010 back to step 1002.

One of ordinary skill in the art will appreciate that method 1000 maybeneficially be used in system 100, e.g., under conditions similar tothose already indicated above in reference to method 800 (FIG. 8).

FIG. 11 shows a flowchart of a method 1100 of operating system 100according to yet another embodiment of the disclosure. Method 1100 maybe implemented using receiver 160. Exemplary steps of method 1100 aredescribed below in reference to FIGS. 1 and 11.

At step 1102 of method 1100, receiver 160 is configured to use (L-R) ofits L spatial-mode channels for data recovery and to use the remaining Rof its L spatial-mode channels for testing the signal-propagationconditions in link 140. As used herein, the term “i-th spatial-modechannel” refers to the hardware in receiver 160 configured to generateoptical signal 166 _(i) and electrical signal 170 _(i). In general, anyof the L spatial-mode channels in receiver 160 can be a training channelor a data-recovery channel. Therefore, at any instant in time, a set ofindices “i” representing the current set of R testing channels may haveR different arbitrary index values selected from the range between 1 andL. The remaining (L-R) index values from this range then represent thedata-recovery channels. In general, receiver 160 is configured so thatthe testing channels address spatial modes of fiber 146 b that aredifferent from the spatial modes addressed by the data-recoverychannels.

At step 1104, receiver 160 is configured to measure a suitableperformance metric (e.g., the signal-to-noise ratio, SNR) correspondingto each of its L spatial-mode channels. Based on the measurementresults, DSP 172 then sorts the spatial-mode channels into two groups.For example, the (L-R) channels having the highest SNR may be placedinto the first group. The R remaining spatial-mode channels are placedinto the second group.

At step 1106, receiver 160 is configured to use the first group ofspatial-mode channels as data-recovery channels and the second group ofspatial-mode channels as testing channels.

At step 1108, receiver 160 reconfigures SM separator 164 to change thespatial modes addressed by the testing channels, while leaving thespatial modes addressed by the data-recovery channels unchanged.Receiver 130 may employ any suitable algorithm for selecting a newsubset of spatial modes for the testing channels. For example, in oneimplementation of method 1100, spatial modes for the new subset may beselected from currently unaddressed spatial modes (e.g., spatial modesthat belong neither to the first group nor to the second group) in arandom manner. The processing of method 1100 is then directed from step1108 back to step 1104.

By cycling through steps 1104-1108, receiver 160 is able to adaptivelychange the spatial modes addressed by the data-recovery channels so thatthese spatial modes include at least some of the best performing spatialmodes of fiber-optic link. As a result, the outage probability isadvantageously reduced compared to that achieved in a staticconfiguration. The cost of this reduction is that the bandwidthcorresponding to the testing channels of receiver 160 is being used forscouting unaddressed spatial modes rather than for transmitting data.

While this disclosure has been described with reference to illustrativeembodiments, this description is not intended to be construed in alimiting sense.

Although various embodiments of the disclosure have been described inreference to multimode fibers, similar principles are also applicable tomulti-core fibers and/or fiber-optic cables.

A communication system may use an optical link having M modes, wherein N(<M) modes are being used for data transmission (e.g., when theprocessors can handle N×N MIMO). The remaining M-N modes may be used forscouting. In this configuration, the transmitter and/receiveraddress(es) all fiber modes, with a first subset of N modes being usedfor carrying information and a second subset of M-N modes being used formonitoring purposes. In one embodiment, one of the methods disclosedherein may be adapted to dynamically change the contents of the firstand second subsets, e.g., by changing a mode designation from “carryingdata” to “scouting,” or vice versa.

As used herein, the term “performance metric” should be construed toencompass any suitable system-performance parameter, such as, withoutlimitation, a BER, an SNR, a constellation quality measure, etc.

Various modifications of the described embodiments, as well as otherembodiments of the invention, which are apparent to persons skilled inthe art to which the invention pertains are deemed to lie within theprinciple and scope of the invention as expressed in the followingclaims.

Unless explicitly stated otherwise, each numerical value and rangeshould be interpreted as being approximate as if the word “about” or“approximately” preceded the value of the value or range.

It will be further understood that various changes in the details,materials, and arrangements of the parts which have been described andillustrated in order to explain the nature of this invention may be madeby those skilled in the art without departing from the scope of theinvention as expressed in the following claims.

The use of figure numbers and/or figure reference labels in the claimsis intended to identify one or more possible embodiments of the claimedsubject matter in order to facilitate the interpretation of the claims.Such use is not to be construed as necessarily limiting the scope ofthose claims to the embodiments shown in the corresponding figures.

Reference herein to “one embodiment” or “an embodiment” means that aparticular feature, structure, or characteristic described in connectionwith the embodiment can be included in at least one embodiment of theinvention. The appearances of the phrase “in one embodiment” in variousplaces in the specification are not necessarily all referring to thesame embodiment, nor are separate or alternative embodiments necessarilymutually exclusive of other embodiments. The same applies to the term“implementation.”

Also for purposes of this description, the terms “couple,” “coupling,”“coupled,” “connect,” “connecting,” or “connected” refer to any mannerknown in the art or later developed in which energy is allowed to betransferred between two or more elements, and the interposition of oneor more additional elements is contemplated, although not required.Conversely, the terms “directly coupled,” “directly connected,” etc.,imply the absence of such additional elements.

The present inventions may be embodied in other specific apparatusand/or methods. The described embodiments are to be considered in allrespects as only illustrative and not restrictive. In particular, thescope of the invention is indicated by the appended claims rather thanby the description and figures herein. All changes that come within themeaning and range of equivalency of the claims are to be embraced withintheir scope.

The description and drawings merely illustrate the principles of theinvention. It will thus be appreciated that those of ordinary skill inthe art will be able to devise various arrangements that, although notexplicitly described or shown herein, embody the principles of theinvention and are included within its spirit and scope. Furthermore, allexamples recited herein are principally intended expressly to be onlyfor pedagogical purposes to aid the reader in understanding theprinciples of the invention and the concepts contributed by theinventor(s) to furthering the art, and are to be construed as beingwithout limitation to such specifically recited examples and conditions.Moreover, all statements herein reciting principles, aspects, andembodiments of the invention, as well as specific examples thereof, areintended to encompass equivalents thereof.

The functions of the various elements shown in the figures, includingany functional blocks labeled as “controllers” or “processors,” may beprovided through the use of dedicated hardware as well as hardwarecapable of executing software in association with appropriate software.When provided by a processor, the functions may be provided by a singlededicated processor, by a single shared processor, or by a plurality ofindividual processors, some of which may be shared. Moreover, explicituse of the term “processor” or “controller” should not be construed torefer exclusively to hardware capable of executing software, and mayimplicitly include, without limitation, digital signal processor (DSP)hardware, network processor, application specific integrated circuit(ASIC), field programmable gate array (FPGA), read only memory (ROM) forstoring software, random access memory (RAM), and non volatile storage.Other hardware, conventional and/or custom, may also be included.Similarly, any switches shown in the figures are conceptual only. Theirfunction may be carried out through the operation of program logic,through dedicated logic, through the interaction of program control anddedicated logic, or even manually, the particular technique beingselectable by the implementer as more specifically understood from thecontext.

It should be appreciated by those of ordinary skill in the art that anyblock diagrams herein represent conceptual views of illustrativecircuitry embodying the principles of the invention. Similarly, it willbe appreciated that any flow charts, flow diagrams, state transitiondiagrams, pseudo code, and the like represent various processes whichmay be substantially represented in computer readable medium and soexecuted by a computer or processor, whether or not such computer orprocessor is explicitly shown.

1. An optical system, comprising: an optical-mode-coupling (OMC) deviceconfigured to address a first subset of spatial modes of an opticallink; and a controller configured to reconfigure the OMC device toaddress a second subset of spatial modes of the optical link duringtransmission of an optical signal carrying data through said OMC deviceand said optical link, wherein the second subset differs from the firstsubset by one or more spatial modes.
 2. The optical system of claim 1,wherein: the optical link comprises a multimode fiber, a multi-corefiber, or a fiber-optic cable; and the OMC device is configured toaddress a subset of spatial modes of said multimode fiber, multi-corefiber, or fiber-optic cable.
 3. The optical system of claim 1, whereinthe data comprises an FEC-encoded block of data or a pilot datasequence.
 4. The optical system of claim 1, wherein the controller isconfigured to cause the OMC device to change the addressing of thespatial modes at a rate that is greater than an inverse of a channelcoherence time corresponding to the optical link.
 5. The optical systemof claim 1, wherein the OMC device is a spatial-mode coupler of anoptical transmitter.
 6. The optical system of claim 5, furthercomprising: an FEC encoder configured to generate a plurality of datastreams carrying an FEC-encoded block of data; and an E/O converterconfigured to convert said plurality of data streams into a plurality ofmodulated optical signals, wherein: the controller is configured tocause the spatial-mode coupler to change one or more spatial modes inthe first subset during transmission through said spatial-mode couplerof said plurality of modulated optical signals; and the spatial-modecoupler is configured to couple each of the modulated optical signals ofsaid plurality into a corresponding spatial mode of the optical linkbelonging to a currently addressed subset.
 7. The optical system ofclaim 6, wherein the FEC encoder is configured to employ an FEC codehaving an FEC block size that causes duration of said transmission ofthe modulated optical signals carrying the FEC-encoded block of data tobe shorter than a channel coherence time.
 8. The optical system of claim1, wherein: the data comprises a pilot data sequence; the optical systemis configured to monitor a performance metric during the transmissionthrough said OMC device and the optical link of the optical signalcarrying the pilot data sequence data; and the controller is furtherconfigured to select the second subset of the spatial modes based on themonitored performance metric and configure the OMC device to address thesecond subset of the spatial modes during transmission through said OMCdevice and said optical link of a second optical signal carrying payloaddata.
 9. The optical system of claim 8, wherein the controller isfurther configured to cause the OMC device to keep the second subsetunchanged until a transmission through said OMC device and said opticallink of a third optical signal carrying a pilot data sequence.
 10. Theoptical system of claim 1, wherein the OMC device is a spatial-modeseparator of an optical receiver.
 11. The optical system of claim 10,wherein: the spatial-mode separator is configured to convert an opticalSDM signal received from said optical link into a plurality of modulatedoptical signals, each of said modulated optical signals corresponding toa respective spatial mode from a currently addressed subset; and theoptical system further comprises: an O/E converter configured to convertthe plurality of modulated optical signals into a correspondingplurality of streams of digital samples; and a digital signal processorconfigured to process the plurality of streams of digital samples torecover data carried by the optical SDM signal.
 12. The optical systemof claim 11, wherein: at sorting times, the optical receiver isconfigured to sort the spatial modes of the currently addressed subsetinto a first group and a second group based on SNR values of thecorresponding modulated optical signals so that the first group hashigher SNR values than the second group; the digital signal processor isconfigured to recover the data carried by the optical SDM signal basedon the streams of digital samples corresponding to the first group ofspatial modes; and between two consecutive sorting times, the controlleris configured to cause the spatial-mode separator to change one or morespatial modes in the second group of spatial modes while keeping thefirst group of spatial modes unchanged.
 13. The optical system of claim12, wherein the controller is configured to: select a first spatial modein the second group corresponding to a lowest SNR value; randomly selecta second spatial mode outside of the currently addressed subset ofspatial modes; and cause the spatial-mode separator to address thesecond spatial mode instead of the first spatial mode.
 14. The opticalsystem of claim 1, wherein the controller is configured to: randomlyselect a first spatial mode from a currently addressed subset; randomlyselect a second spatial mode outside of the currently addressed subset;and cause the OMC device to address the second spatial mode instead ofthe first spatial mode.
 15. An optical system, comprising: anoptical-mode-coupling (OMC) device configured to address a first subsetof spatial modes of an optical link for carrying data and a secondsubset of spatial modes of the optical link for monitoring a performancemetric, wherein the first subset and the second subset taken togetherinclude all guiding modes of the optical link; and a controllerconfigured to reconfigure the optical system to change at least one ofthe first and second subsets during transmission of an optical signalcarrying data through said OMC device and said optical link.
 16. Amethod of processing optical signals, the method comprising: configuringan optical-mode-coupling (OMC) device to address a first subset ofspatial modes of an optical link; and changing one or more spatial modesin the first subset while transmitting through the OMC device and saidoptical link an optical signal carrying data.
 17. The method of claim16, wherein the data comprises an FEC-encoded block of data or a pilotdata sequence.
 18. The method of claim 16, wherein: said changingincludes changing spatial modes at a rate that is greater than aninverse of a channel coherence time corresponding to said optical link;and the method further comprises selecting the rate so as to subject aportion of the optical signal carrying an FEC-encoded block of the datato an effective state of the optical link that approximates an averagestate of the optical link.
 19. The method of claim 16, furthercomprising: monitoring a performance metric during transmission throughsaid OMC device and said optical link of the optical signal carrying apilot data sequence; selecting a subset of the spatial modes based onthe monitored performance metric; configuring the OMC device to addressthe selected subset during transmission through said OMC device and saidoptical link of a second optical signal carrying payload data; andkeeping the selected subset unchanged until a transmission through saidOMC device and said optical link of a third optical signal carrying apilot data sequence.
 20. The method of claim 16, further comprising: atsorting times, sorting the spatial modes of a currently addressed subsetinto a first group and a second group based on SNR values ofcorresponding modulated optical signals so that the first group hashigher SNR values than the second group; and recovering the data byprocessing the modulated optical signals corresponding to the firstgroup of spatial modes, wherein said changing comprises: between twoconsecutive sorting times, changing one or more spatial modes in thesecond group of spatial modes while keeping the first group of spatialmodes unchanged.